Finally, as a consistency check of the constructed basis,
we compared it with the operator counts for a given field content
that were derived using the conformal Hilbert series
method [1]}, [2]}, [3]}. This
approach allows for a systematic group-theoretic treatment of
equations of motion and inclusion of integration-by-parts identities. It calculates
an object called the Hilbert series, given by
\(H(\mathcal {D}, \phi _1, \dots , \phi _N) = \sum \limits _{k,r_1,\dots ,r_N} \, c_{k,r_1,\dots ,r_N}\; \phi ^{r_1}_1 \dots \phi ^{r_N}_N \;\mathcal {D}^k,\) 
